Information Technology Reference
In-Depth Information
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0
0.02
0.04
0.06
0.08
0.1
Fig. 5.9. Value of the exponent as a function of the noise intensity for the GRN for the oral
development of Arabidopsis thaliana. We have preserved the topological structure but muted the
Boolean rules with a certain probability. Each set of points corresponds to dierent probabilities
(from top to bottom 0.00, 0.02, 0.04, 0.10, 0.20, and 0.50). Even with the same probability, each
single mutation can give rise to very dierent outputs. For this reason, we have averaged over
initial conditions (as usual) and over mutations with the same probability. Fluctuations are hence
quite remarkable in this plot, but we have preferred to removed them to preserve the clarity of the
results. The horizontal line corresponds to the 1=f noise.
rules. We allow for violations of the rules with certain probability and look at the
exponent of the time series of the generated uctuations. Mutations are performed
with certain probability p; dierent realizations for the same value of p gives rise ob-
viously to dierent rules, but these precise implementations of the rules can make
huge changes in the number of attractors and in the structure of their basins of
attraction. Then the response of the system depends not only on the value of p
but also on the single realization of the mutation. For this reason, when plotting
in Fig. 5.9 the exponent as a function of p, every single point is an average over
dierent realizations (apart from an average over dierent initial conditions as we
have done in the simple model), but with large uctuations (not shown in the plot).
In Fig. 5.9 it is clear that as the mutation probability increases the response
of system moves away from the 1=f noise behavior, and the resulting systems are
not able to show the variety of behaviors we have observed in the network with the
original rules or in the simple model of the rst part of our work. A more detailed
analysis of how the alteration of logical rules aects the visitation of the attractors
and the noise spectra is still needed.
